Inequalities for Hyperbolic Functions and Their Applications
A basic theorem is established and found to be a source of inequalities for hyperbolic functions, such as the ones of Cusa, Huygens, Wilker, Sandor-Bencze, Carlson, Shafer-Fink type inequality, and the one in the form of Oppenheim's problem. Furthermore, these inequalities described above wi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/130821 |
| _version_ | 1818491073678278656 |
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| author | L. Zhu |
| author_facet | L. Zhu |
| author_sort | L. Zhu |
| collection | DOAJ |
| description | A basic theorem is established and found to be a source of inequalities for hyperbolic functions, such as the ones of Cusa, Huygens, Wilker, Sandor-Bencze, Carlson, Shafer-Fink type inequality, and the one in the form of Oppenheim's problem. Furthermore, these inequalities described above will be extended by this basic theorem. |
| first_indexed | 2024-12-10T17:25:26Z |
| format | Article |
| id | doaj.art-4d3e510e24154c6d84f823b38d1dc59b |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-10T17:25:26Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-4d3e510e24154c6d84f823b38d1dc59b2022-12-22T01:39:52ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-01201010.1155/2010/130821Inequalities for Hyperbolic Functions and Their ApplicationsL. ZhuA basic theorem is established and found to be a source of inequalities for hyperbolic functions, such as the ones of Cusa, Huygens, Wilker, Sandor-Bencze, Carlson, Shafer-Fink type inequality, and the one in the form of Oppenheim's problem. Furthermore, these inequalities described above will be extended by this basic theorem.http://dx.doi.org/10.1155/2010/130821 |
| spellingShingle | L. Zhu Inequalities for Hyperbolic Functions and Their Applications Journal of Inequalities and Applications |
| title | Inequalities for Hyperbolic Functions and Their Applications |
| title_full | Inequalities for Hyperbolic Functions and Their Applications |
| title_fullStr | Inequalities for Hyperbolic Functions and Their Applications |
| title_full_unstemmed | Inequalities for Hyperbolic Functions and Their Applications |
| title_short | Inequalities for Hyperbolic Functions and Their Applications |
| title_sort | inequalities for hyperbolic functions and their applications |
| url | http://dx.doi.org/10.1155/2010/130821 |
| work_keys_str_mv | AT lzhu inequalitiesforhyperbolicfunctionsandtheirapplications |